Baroque music is the music of the Western European world around the year 1700
(say, between 1650 and 1750 or so) -- i.e., the music of J.S. Bach, Lully,
Francois Couperin, Handel, and contemporary composers. It is the music
of one of the greatest periods of renewal, growth and expansion of European
culture and science.

Baroque music is often rather interesting rhythmically. Especially
in Baroque music with some French infuence in it -- such as in the so-called
``suites'' (also in those by non-French Baroque composers) --, there are very
often remarkable and interesting rhythmical patterns incorporated into the
structure of the music. When present, this rhythmical ``play''
represents a significant part of what makes the music interesting. When
playing (or listening to) Baroque music in which these rhythmical things are
present (such as ``suites''), it is in my opinion therefore a shame to
overlook these rhythmical features.

These rhythmical features in many Baroque pieces seem to have originated from
French renaissance dances. All of the interesting rhythmical patterns in
Baroque music (which are discussed and examples of which are given further
below) consist in the fact that the pieces do not use a regular beat as is the
case as most ``classical'' music as well as in almost all modern pop
music. Instead, much Baroque music constantly alternates groups of two
beats and groups of three beats. These ``strange'' rhythmical patterns
in Baroque music, consisting of such non-homogeneous groups of beats, are
however in Baroque music always combined into larger patterns, which repeat
over and over. I.e., the ``strange'' rhythm is included inside a pattern
of 8 to 16 beats or so, and all over a longer section of a piece this
rhythmical pattern constantly repeats. (However, of course sometimes the
rhythmical pattern does change between two larger sections of a single
piece). For example, a piece may consist of phrases of 8 beats each of
which is subdivided into 3 + 3 + 2; or it may consist for example of phrases
of 12 beats each of which is subdivided into 3 + 2+2+2 + 3.

To people who are not musicians, the last paragraph above might sound rather
mystical. Therefore I'll now explain first what all this stuff about
``beats'' and ``measures'' means. (Musicians might skip to the next section.)

Almost all music, when we look at the time aspect or rhythmical aspect of the
music, naturally is thought of as having or being superposed on a regular
``beat'' or ``count'', like the ticks of a clock ticking, or like the beat of
the human heart. In fast music, the beats or counts are short and
succeed each other quickly; in slow music, the beats are of longer duration
and succeed each other slowly. The rate of beats in music that is felt
to have a comfortable, relaxed pace, is about equal to the rate of the beats
of the human heart. (Yes, it's clear that music, like most in human
culture, exhibits rather many anthropocentric features.)

In most music, such as European ``classical'' music and also modern pop music,
these counts are naturally grouped into groups of two, three, four, (seldom)
five, six or more beats -- these groups are called ``bars'' or
``measures''. (The word ``bar'' seems to be related from the practice of
separating measures in printed musical notation with vertical bar-lines
between them to make the printed musical notation more easily interpretable
visually.) The first beat in each measure is always sounded somewhat
more loudly or more intensely as the other beats in the measure. Or,
looked at from the other side of things, the strong beat is always thought of
as being the first beat in the measure. It is said that this first beat
gets the ``accent'', or that this is the one that ``gets the beat''.
This is fully similar to the accent of intensity (or ``stress'') in human
speech, i.e., the phenomenon that in words of more than one syllable only one
syllable gets the (strongest) accent. In music using sung text, the
music is composed in such a way that the accents in the words exactly line up
with the strong beats in the music. In the vast majority of music, each
piece of music, or each longer section of a piece of music, uses the same
length of measures throughout: i.e., the rhythm of the piece consists of
rhythmically identical measures which constantly repeat -- in other words, the
beats or counts that are accented constantly fall in regular, periodical,
places; i.e., every 2nd beat is accented in a piece with a 2-beat measure,
every 3rd beat is accented in a piece with a 3-beat measure, and so on.

In measures of more than 2 or 3 beats in length, there is often a
``secondary'' accent. This is like very long words in human speech often
getting, apart from a main accent of stress, also a secondary accent; for
example in the word ``incomprehensible'' where the main accent is on
``-hen-'', but where there is also a second accent of intensity, but a weaker
one, on ``in-''. Most modern pop music has measures of 4 beats length,
where there is a secondary accent on every 3rd beat in every measure.
Many classical music has measures of 6 beats -- these can either be measures
with a secondary accent on the 4th beat which therefore exhibit an internal
sub-structure in each measure consisting of two ``sub-measures'' of each 3
beats, like this:

or they can be measures showing a
sub-structure consisting of ``sub-measures'' of two beats in length which
therefore have the secondary accents on the 3rd and 5th beat of the 6-beat
measure:

| o o o o o o | o o o o o o | ...
>> > > >> > >

The fist kind of 6-beat measure is often schematically represented as ``3+3'',
the second one as ``2+2+2''.

The kind or type of measure a piece of music has is termed the
``meter'' of the piece. When the measures of a piece each contain
two beats or when the measures are composed of two (equally large) parts like
the first kind of 6-beat measure above (the 3+3 one), then we say that the
meter of the piece is a ``duple meter''. When the measures of a
piece each contain three beats or when the measures are composed of 3 (equally
large) parts like the second kind of 6-beat measure above (the 2+2+2 one),
then we say that the meter of the piece is a ``triple meter''.
Most pieces of have a kind of meter that allows it to be classified as either
duple- or triple-meter pieces. However, meters with for example 5 or 7
beats per measure (which are anyway rather rare), cannot be classified as
either duple- or triple-meter pieces (... well, at least not in a
straightforward way :-)).

It seems that much Baroque music is loaded with all sorts of such rhythmical
``jokes'' and inventivity. Those 17th and 18th century people seem to
have had an urge to insert lots of ``mathematical'' ingenuities into the
music... It seems that these people may have had a in some way a
distaste for things that were too simple, too un-artificial, and too
intuitively or too blatantly obvious; and that in those times people rather
enjoyed all kinds of artificial ``constructions''. Looking at other
aspects of 17th and 18th century culture, to my mind the love for and pleasure
in mechanical constructions is obvious. I do imagine that I perceive a
kind of ``carry over'' from this love for mechanical constructions into
features of Baroque music -- but, well, all this interpretation stuff and all
this association between music and other items of culture is maybe only my own
guess, and is perhaps not very solidly funded. But it remains a fact
that -- whatever the cultural significance or background of these rhythmical
oddities is -- that very much Baroque music does exhibit rather interesting
and remarkable rhythmical patterns.

These rhythmical features or counter-rhythms in much Baroque music give the
music a kind of dynamic, energetic flavour. It is as if, instead of
being content with lazily trudging on in always the same dull rhythm, the
musicians have too much energy which they cannot refrain from letting burst
out on regular intervals by throwing in a rhythmical somersault, after each of
which they simply fall back with a straight face into the old rhythm as if
nothing strange had happened.

Note that despite these rhythmical tricks, the beats themselves always keep
having the same length (duration) and rate. The basic clock-tick or
heart-beat of the music simply keeps on going evenly. It is only the
grouping of the beats into groups of two/three/four beats where each 1st beat
of such a group gets the strong accent, that is changed in the course of the
music. Alternatively expressed, the places where some of the accents
fall are changed from their normal positions where we would have expected them
regarding the periodicity suggested by the barlines in the printed
music.

For all Baroque music, when written down in musical notation, a regular
barring is always used, i.e. with a bar-line e.g. every three or four beats,
precisely as in ``classical'' music or modern pop music. The rhythmical
``play'' in Baroque music is therefore unfortunately not immediately visually
apparent from the way in which the music is written down in musical
notation. The placement of the barlines in the printed music is regular,
the places where the actual accents fal in the music is somewhat less
regular. Nevertheless, the barlines in the printed music do show the
larger lines of the music; the interesting rhythmical patterns with which the
is text is concerned have to be thought of as small local variations on the
larger, steady, beat of the piece. Normally, when playing a piece of
Baroque music in which interesting rhythmical things happen, one just keeps
counting mostly in the way indicated by the printed barlines. The
barlines occurring at regular intervals are simply more convenient to keep
track of the overall timing and are less confusing to work with than barlines
at irregular intervals would be.

All of the ``interesting'' rhythmical patterns in Baroque music consist in
placing accents that introduce grouping in 2-beat-sized groups in tiple meters
and in 3-beat-sized groups in duple meters. Expressed in another way:
rhythms using groups of two beats (in each of which the 1st beat is accented
and the other is not accented) are often present in triple-meter music; and
rhythms using groups of 3 beats (in each of which the 1st beat is accented and
the other two are not) are often present in duple-meter music. These
things therefore intruduce a temporary or ``local'' deviation from the
normal rhythm -- temporarily, a ``counter-rhythm'' is used.

Most often, these temporary ``counter-rhythms'' occur periodically and
regularly themselves, throughout the piece of Baroque music. That is,
the changes in rhythm periodically repeat, and therefore there is incorporated
in the music a pattern of rhythm which repeats over and over throughout
the piece.

The pattern of 2-beat subgroupings in triple-meter Baroque pieces is often
like this:

In the last diagram above, I've just arbitrarily thrown in barlines every 4
beats -- I could have also put in the barlines every two or 8 beats
instead. This would not have made any difference for the position of
beats, accents and \____/ brackets in the diagram -- the same diagram
would still show the correct accents also with those (partly) different other
bar-lines.

Note that in the the above examples it is indeed plausible in some respects to
speak of a regular alternation between a duple and a triple meter.
However, it nevertheless remains the case that only one of the meters is
``felt'' to be the ``normal'' meter of the piece -- this is the meter the
piece is notated in as regards bar-lines and as regards the ``time signature''
(= meter indication (e.g. 3/4 for triple meter with each beat being ``1/4
note'')) written at the start of the piece. This ``normal'' meter is
felt to be the ``background'' into which the ``counter-rhythm'' occasionally
intrudes. The ``counter-rhythm'' is felt as as temporary deviation that
is set off against or superposed on the ``normal'' meter. While
listening to the piece, it is as if even during the rhythmical anomalies, one
hears the normal rhythm ticking on even when it is temporarily not overly
expressed. Therefore, despite the fact that in some ways it is possible
to speak of an alternation of two types of meters, nevertheless those two
measures do not enjoy equal ``status'', or ``weight'', or ``function''.

Such ``counter-rhythms'' set off against the main or ``background'' rhythm of
the piece are commonly called ``hemiolas''. This is an
old-fashioned musical term originating from the Greek hemi = half, and
holos = whole. Any kind of local ``counter-rhythm'' in music is
called a ``hemiola'', whether the counter-rhythm consists of groups of 2 beats
in triple meters, or groups of 3 beats in duple meters, or any other kind of
``counter-rhythm''.

All the types of baroque music in which interesting rhythmical patterns are
present which repeat periodically, are always pieces which consist of a
regular structure in terms of ``phrases''.

A ``phrase'' is a small portion of the piece, mostly a few bars long, which is
like a single line (or ``verse'') in an old-fashioned poem (not a free verse
poem). In the poem, all the verse-lines often have a similar structure
(e.g. same number of syllables, same pattern of accents on those
syllables). The same pattern is repeated in each line, but the actual
words through which the pattern is realized are different in each line.
The poem as a whole can be thought of as a collection of verse lines put
together in such a way that the total exhibits satisfying, interesting and/or
pleasing proportions.

It is the same in the Baroque pieces which show a regular phrasing
structure. Many aspects of the harmonic and rhythmical pattern in all
phrases of the piece are similar, and the phrases can be throught of as
repeats of this same underlying pattern, which is however mostly realized in
each succeeding phrase in a partly different way, e.g. by slight variations in
rhythm, by playing the same harmonic theme in a different pitch, by filling in
or embellishing the tune with small short notes, by conversely leaving out
some notes, by putting in extra contrapuntal voices, and so on.

Most often, all verses in poetry and also all phrases in music are of the same
length throughout the poem or piece of music. A menuet, for example,
consists of phrases of 8 bars of 3 beats each. The menuet as a whole
consists simply of a sequence of such phrases of 8 bars each. The basic
harmonic and rhythmical pattern in this phrase is repeated in all the
phrases.

However, in some forms of poems as well as (Baroque and other) music, the
phrases are not all of the same lenght or internal structure. A
limerick, for example, consists of 3 long phrases and 2 short ones.
There are similar examples in music. In these cases, nevertheless, there
still is a pattern that is present in the phrase (or verse) structure of the
piece (or poem).

Apart from the possibility of having different types of phrase in the
piece of musici, which are played in an order of sequence which forms a
definite pattern, there is also the possibility of sub-phrases being present
inside phrases: i.e., phrases can also be nested hierarchically inside
other phrases. The phrasing aspect of a piece of music is
definitely a part of what makes a piece of (Baroque) music interesting.
A significant part of the aethetic and intellectual pleasure of hearing
and playing such a piece resides in the play with these phrasing
patterns -- similar as the tune, instrumental or vocal sound, harmony,
and so on are aspects of what make a piece of music interesting.

The phrases of a piece of music can be regarded as the sentences in a text of
natural language. Longer compound sentences can be made up of smaller
subordinate sentences. Between sentences of text, at the full stops,
there is felt to be a pause -- it is the same in music, where between phrases
there is felt to be a kind of ``breathing space'' between the end of the first
phrase and the start of the second. . In vocal music, the words of
the music are most often placed in such a way into the music by the composer
that the sentences of the text coincide with the phrases of the music; and in
vocal music, singers inhale breath between phrases of the music. Between
smaller sub-phrases in the music, there are felt to be smaller ``breathing
spaces'' similar to commas in a sentence of text. The phrasing of a
piece of music is similar to the interpunction of a text of natural
language.

The phrasing structure of a piece of music is another part of the rhythmical
side of the piece, hence it is logical that the phrasing of a piece and its
rhythmical patterns are important to each other. Apart from forming a
``substrate'' for play that is interesting and easthetic in its own right, the
rhythmical patterns in Baroque music also serve to make the phrase structure
of the piece more clear. Each phrase (or type of phrase) most often has
its disctinctive rhythmical pattern.

Most of the Baroque pieces in which interesting ``counter-rhythms'' are
present are pieces which also have a fairly rigid phrase structure. The
rhythmical pattern imposed or added on to the basic beat of the piece, repeats
in each successive phrase. To figure out the rhytmical aspects of a
piece, it is necessary to have a clear picture about how the phrase structure
of the piece fits together. But conversely, hearing some familiar
rhythmical pattern happen in a piece, is also a help towards uncovering the
piece's phrase structure.

Most Baroque pieces in which interesing rhythmical things are happening are
the so-called ``dance-forms'' in ``suites'', such as menuets, allemandes,
gavottes, and so on. However, many Baroque pieces which are not labelled
as any of the ``dance forms'', do nevertheless exhibit the phrasing and
rhythmical characteristics of one of the ``dance forms''. In pieces
often called ``fantasies'', it also occurs that some newly invented variant or
amalgam of the ``dance-form'' rhythms and phrase structures is used.

Some of the dance forms which use triple meters are:

Menuets. Each phrase is 8 bars long, each bar consists of 3
beats. The sequence of 8 bars forming a phrase always is made up out of
two sub-phrases of 4 bars each. In most menuets, the first of these two
sub-phrases is further divided into two small phases of 2 bars each, but the
second of two sub-phrases of 4 bars is a unit as a whole and has a
``counter-rhythm'' pattern precisely in the middle of it. The
first two sub-phrases of 2 bars are often much alike, and are e.g. repeats
of the same harmonic ``theme''; and the phrase of 4 bars at the
end forms a kind of ``finale'' to the whole 8-bar phrase. Like this:

Endings. At this point, it is expedient to insert a small
diversion into this section on ``dance forms''. The above pattern of 4
bars of 3 beats each, the middle two bars of which form a hemiola of 2+2+2
beats, is a kind of ``standard pattern'' in triple meter Baroque music.
Very, very often, endings of triple meter pieces which are not ``dance forms''
and which otherwise do not show remarkable rhythmical features, are made up of
precisely this 4-bar rhythmical pattern:

This happens often even in post-Baroque pieces in Western ``classical''
music. In Handel (who is a late-Baroque composer), this ending occurs in
nearly all triple-meter pieces. This rhythmical pattern could be said in
some ways to serve as a kind of ``signal'' with the meaning ``this is the end
of the piece''; in this way it is similar to the very familiar and pervasive
variants dominant-septime chord sequences in endings of music. These
harmonic and rhythmical patterns seem to help to give the listener the
necessary idea of ``satisfaction'' and ``conclusiveness'' at the end of a
piece.

We now go on with some other examples of triple-meter ``dance-forms''.

Gigues. Gigues are triple-meter pieces in which the
phrases are 4 bars long, each bar having 3 beats. Our familiar
``standard pattern'' occurs in each of these 4-bar phrases, in its familiar
position right in the middle of the phrase, like this:

This is the same diagram as the 2nd one in the section above on menuets, but
note that in the gigue, the ``counter-rhythm'' is present in each phrase of 4
bars. As we see from the above diagram, this has as a result that
actually half of the bars of the piece have this ``counter-rhythm'' imposed on
them, and also that there is a constant and regular alternation between
sections of 6 beats of triple-meter and sections of 6 beats of
duple-meter. In gigues, however, the triple meter is always still
everywhere firmly the most promiment rhythm -- the duple-meter sections are
felt to be slight local features added on top of the on-going triple-meter
beat which always stays firmly in charge; it is not felt that the duple meter
actually temporarily sometimes takes over from the triple meter.

Courantes. This same regular alternation between 6 beats of
triple meter and 6 beats of duple meter is present in courantes.
Courantes are among the most rhythmically interesting kinds of Baroque
pieces. Basically, the rhythmical pattern of most courantes is the same
as that of the gigue as shown above, and the length of the phrases in
courantes is also 12 beats as in gigues. However, courantes are written
down most often in 6-beat meters (which makes each phrase therefore 2 bars
long); and the start and end of the phrases relative to the basic beat of the
piece, and the position of the ``counter-rhythm'' within the phrases, is often
different in courantes than in menuets and gigues. Courantes, when
written in 6-beat meters, always basically have one 6-beat bar of triple meter
(i.e., 3+3), alternating with one 6-beat bar of duple meter (i.e.,
2+2+2). The duple-meter sections always entirely fill the 6-beat
measure, and are present only within these bars. Thus:

The alternation between a bar of 2+2+2 and a bar of 3+3 is the hallmark of a
courante. In the courante, in the duple meter bars, the duple meter does
entirely take over from the triple meter. The courante seems to be the
kind of piece in which two competing rhythms are treated with the most
equality. Listening to a courante, it is in fact often very hard to
decide whether the piece predominantly has a duple or a triple
meter ! The listener very often experiences a kind of interesting
indeterminacy as to what bar is intended to be in duple meter and what bar in
triple meter. In my opinion, this is an aspect of the courante form that
is often used by composers to make their courante pieces more
interesting. The courante in a way could perhaps be said to be a piece
that maximizes the ``play'' with competing triple and duple meters in the same
piece.

The actual position of the phrases (which are always 12 beats long) within
this rhythmical pattern, i.e., the position of the ``full stops'' between the
phrases within the above rhythmical pattern, is often different between
different courantes. The phrases can begin with a duple-meter section,
but in other courantes the phrases can begin with a triple-meter
section. Therefore, the piece as a whole can either begin with a
duple-meter section or with a triple-meter section. When studying a new
piece from printed music, some experimentation may be necessary to determine
what seems to ``fit'' or ``sound'' best. However, it is always the case
that within the same piece, the basic phrase structure, is fixed and is
basically repeated over and over.

There do however often occur variations on the rhythmical structure within a
courante, often in the middle of the piece, such as insertion of 12-beat long
sections with either a duple or triple meter throughout, or a repeat of the
final 6-beat half of a preceding phrase. After such a rhythmical
``excursion'' however, the initial rhythmical and phrasing pattern is always
resumed again to finish the piece.

Some of the dance forms which use duple meters are:

Gavottes. Gavottes have phrases of 8 beats long each.
Regarding the quick pace of gavottes, these phrases are rather short in
duration; most often these 8-beat phrases occur in pairs which together form
longer phrases of 16 beats. Gavottes are written in bars with 4 beats
each. The ``full stops'' between 8-beat phrases occur exactly in the
middle of a bar. The phrasing and rhythmical struture is like this:

Often, the ``counter-rhythm'' in the second 8-beat sub-phrase of a 16-beat
section seems to be more marked than in the first 8-beat sub-phrase, in which
case the first 8-beat sub-phrase also often is built up out of two successive
4-beat sub-phrases; in that case, we therefore have the following pattern in
the 16-beat phrase:

Note that, interestingly, this last pattern effectively forms an entirely
complementary version of the menuet rhythmical pattern: duple and triple
metric patterns are exchanged troughout and play complementary roles.

Allemandes. These have phrases of 16 beats long.
In most pieces, they are notated in bars of 4 beats long.
The rhythmical and phrasing pattern in allemandes is like this:

After this, the 16-beat rhythmical pattern repeats. Note how the 6-beat
hemiola pattern sits right in front of the final beat of the phrase (=
the beat that gets a final chord), as it always does.

In the middle of a piece, however, it often occurs that phrases of half the
above length, i.e., of 8 beats instead of 16 beats, are used.
Potentially, each of those can get the hemiola rhytm pattern, either strongly
or weakly expressed. It is therefore possible that two of such 8-beat
phrases that each show the hemiola rhythm succeed each other directly, like
this:

Note carefully that in Bach's allemande notation, the heavy final beat of the
phrase , remarkably enough, falls right in the middle of an 8-beat bar, and
that the 6-beat hemiola patterns always straddle barlines.